A collisionless singular cucker-smale model with decentralized formation control

Young Pil Choi, Dante Kalise, Jan Peszek, Andres A. Peters

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)

Abstract

We address the design of decentralized feedback control laws inducing consensus and prescribed spatial patterns over a singular interacting particle system of Cucker-Smale type. The control design consists of a feedback term regulating the distance between each agent and preassigned subset of neighbors. Such a design represents a multidimensional extension of existing control laws for 1D platoon formation control. For the proposed controller, we study consensus emergence, collision-avoidance, and formation control features in terms of energy estimates for the closed-loop system. Numerical experiments in 1, 2, and 3 dimensions assess the different features of the proposed design.

Original languageEnglish
Pages (from-to)1954-1981
Number of pages28
JournalSIAM Journal on Applied Dynamical Systems
Volume18
Issue number4
DOIs
Publication statusPublished - 2019

Bibliographical note

Funding Information:
\ast Received by the editors January 30, 2019; accepted for publication (in revised form) by M. Chaves August 29, 2019; published electronically November 7, 2019. https://doi.org/10.1137/19M1241799 Funding: The first author's research was supported by NRF grants 2017R1C1B2012918 and 2017R1A4A1014735 and a POSCO Science Fellowship of the POSCO TJ Park Foundation. The third author's research was supported by Polish MNiSW grant Mobilnosc Plus 1617/MOB/V/2017/0 and by NSF grant RNMS11-07444 (KI-Net). The fourth author's research was supported by the Advanced Center for Electrical and Electronic Engineering, Basal Project FB0008, and by grant FONDECYT 3160738, CONICYT Chile. \dagger Department of Mathematics, Yonsei University, Seoul 03722, Republic of Korea (ypchoi@yonsei.ac.kr). \ddagger School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2QL, UK (dante. kalise@nottingham.ac.uk). \S Center for Scientific Computation and Mathematical Modeling (CSCAMM), University of Maryland, College Park, MD 20742-4015, and the Institute of Mathematics of the Polish Academy of Sciences, 00-656 Warsaw, Poland (j.peszek@mimuw.edu.pl). \P Departamento de Electricidad, Facultad de Ingenier\{\i'}a, Universidad Tecnolo\'gica Metropolitana, 7800002, Santiago, Chile (a.petersr@utem.cl).

Funding Information:
The first author's research was supported by NRF grants 2017R1C1B2012918 and 2017R1A4A1014735 and a POSCO Science Fellowship of the POSCO TJ Park Foundation. The third author's research was supported by Polish MNiSW grant Mobilnosc Plus 1617/MOB/V/2017/0 and by NSF grant RNMS11-07444 (KI-Net). The fourth author's research was supported by the Advanced Center for Electrical and Electronic Engineering, Basal Project FB0008, and by grant FONDECYT 3160738, CONICYT Chile. DK and AP wish to dedicate this paper to the memory of Mario Salgado Brocal.

Publisher Copyright:
© 2019 Society for Industrial and Applied Mathematics

All Science Journal Classification (ASJC) codes

  • Analysis
  • Modelling and Simulation

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